246 NOTE ON THE INEQUALITY IN THE MOON'S LATITUDE [29 



are composed of periodic terms which have short periods compared with 

 the time of revolution of the Moon's node that is, with the period of the 



sm(N-C) and cos(N-C). 

 Hence in integrating we may at first neglect the terms 



. 5Ar *- 



-j-^., -,.- i and l-f^ }oN, -,. ^, 

 \dN/ \di / \dNJ \di / 



leaving them to be taken into account, if necessary, in a subsequent 

 approximation. 



For the same reason we may suppose cot i to be constant in integrating, 

 and we may take 



dN 



omitting the periodic term F(B, 6'}; and we may also suppose that to and 

 C are constants. 



With these simplifications, we have 



dSN . .~. . . . 



Y = c sm 1 01 + CD cot i sin (N C), 



dSi u> dN 



- as- -. COS (N - C) ~j- . 



at c cos * ' at 



From the latter of these equations 



C COS I 



sin (JV- C), 



and substituting this value of Si in the former, we find 



dt 



* Sm (NC) + (d cot i sin (^V C), 



=B _^_^__. B in(jV_C f ), 



sin i cos i 



c sin * 



dN 



and therefore BN=- r .cos(N-C] 



c sin i cos t 



